source: ThirdParty/levmar/src/expfit.c@ 1ba51c

////////////////////////////////////////////////////////////////////////////////////
//  Example program that shows how to use levmar in order to fit the three-
//  parameter exponential model x_i = p[0]*exp(-p[1]*i) + p[2] to a set of
//  data measurements; example is based on a similar one from GSL.
//
//  Copyright (C) 2008  Manolis Lourakis (lourakis at ics forth gr)
//  Institute of Computer Science, Foundation for Research & Technology - Hellas
//  Heraklion, Crete, Greece.
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
////////////////////////////////////////////////////////////////////////////////////

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#include <levmar.h>

#ifndef LM_DBL_PREC
#error Example program assumes that levmar has been compiled with double precision, see LM_DBL_PREC!
#endif


/* the following macros concern the initialization of a random number generator for adding noise */
#undef REPEATABLE_RANDOM
#define DBL_RAND_MAX (double)(RAND_MAX)

#ifdef _MSC_VER // MSVC
#include <process.h>
#define GETPID  _getpid
#elif defined(__GNUC__) // GCC
#include <sys/types.h>
#include <unistd.h>
#define GETPID  getpid
#else
#warning Do not know the name of the function returning the process id for your OS/compiler combination
#define GETPID  0
#endif /* _MSC_VER */

#ifdef REPEATABLE_RANDOM
#define INIT_RANDOM(seed) srandom(seed)
#else
#define INIT_RANDOM(seed) srandom((int)GETPID()) // seed unused
#endif

/* Gaussian noise with mean m and variance s, uses the Box-Muller transformation */
double gNoise(double m, double s)
{
double r1, r2, val;

  r1=((double)random())/DBL_RAND_MAX;
  r2=((double)random())/DBL_RAND_MAX;

  val=sqrt(-2.0*log(r1))*cos(2.0*M_PI*r2);

  val=s*val+m;

  return val;
}

/* model to be fitted to measurements: x_i = p[0]*exp(-p[1]*i) + p[2], i=0...n-1 */
void expfunc(double *p, double *x, int m, int n, void *data)
{
register int i;

  for(i=0; i<n; ++i){
    x[i]=p[0]*exp(-p[1]*i) + p[2];
  }
}

/* Jacobian of expfunc() */
void jacexpfunc(double *p, double *jac, int m, int n, void *data)
{   
register int i, j;
  
  /* fill Jacobian row by row */
  for(i=j=0; i<n; ++i){
    jac[j++]=exp(-p[1]*i);
    jac[j++]=-p[0]*i*exp(-p[1]*i);
    jac[j++]=1.0;
  }
}

int main()
{
const int n=40, m=3; // 40 measurements, 3 parameters
double p[m], x[n], opts[LM_OPTS_SZ], info[LM_INFO_SZ];
register int i;
int ret;

  /* generate some measurement using the exponential model with
   * parameters (5.0, 0.1, 1.0), corrupted with zero-mean
   * Gaussian noise of s=0.1
   */
  INIT_RANDOM(0);
  for(i=0; i<n; ++i)
    x[i]=(5.0*exp(-0.1*i) + 1.0) + gNoise(0.0, 0.1);

  /* initial parameters estimate: (1.0, 0.0, 0.0) */
  p[0]=1.0; p[1]=0.0; p[2]=0.0;

  /* optimization control parameters; passing to levmar NULL instead of opts reverts to defaults */
  opts[0]=LM_INIT_MU; opts[1]=1E-15; opts[2]=1E-15; opts[3]=1E-20;
  opts[4]=LM_DIFF_DELTA; // relevant only if the finite difference Jacobian version is used 

  /* invoke the optimization function */
  ret=dlevmar_der(expfunc, jacexpfunc, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // with analytic Jacobian
  //ret=dlevmar_dif(expfunc, p, x, m, n, 1000, opts, info, NULL, NULL, NULL); // without Jacobian
  printf("Levenberg-Marquardt returned in %g iter, reason %g, sumsq %g [%g]\n", info[5], info[6], info[1], info[0]);
  printf("Best fit parameters: %.7g %.7g %.7g\n", p[0], p[1], p[2]);

  exit(0);
}